Evaluate the series 1 + z + z²/2 + z³/6 + .. + z^n/n! + ... at point z=iπ?

4 ⤊

2007-12-10 04:11:13 · 3 answers · asked by Alexander 6 in Science & Mathematics ➔ Mathematics

1 + z + z²/2 + z³/6 + .. + z^n/n! + ...
= e^z
= e^(iπ)
= cos π + i sin π
= -1.

2007-12-10 04:25:37 · answer #1 · answered by Madhukar 7 · 3⤊ 0⤋

This series is the expansion of e^z and is
good everywhere.So the series evaluated
at z = iÏ = -1.

2007-12-10 12:31:15 · answer #2 · answered by steiner1745 7 · 1⤊ 0⤋

This is the expansion of e^z.
at z=iPI, it is e^iPI

2007-12-10 12:22:54 · answer #3 · answered by cidyah 7 · 0⤊ 0⤋